4 Overview of Long-Run Economic Growth

Question 1

Define growth rate

Answer 1

A growth rate in some variable y is the percentage change in that variable between two points in time.

Question 2

Equation for growth rate (national income)

Answer 2

Question 3

Equation for income (involving growth rate)

Answer 3

Question 4

What is the Rule of 70?

Answer 4

Question 5

What is a ratio scale?

Answer 5

A plot where equally spaced tick marks on the vertical axis increase by a constant ratio each time (e.g. 1, 2, 4, 8, 16).

Question 6

What does a ratio scale tell us about the growth rate?

Answer 6

If the ratio scale line is linear, the growth rate is constant.

If concave, the growth rate is decreasing.

If convex, the growth rate is increasing.

Question 7

Useful properties of ratios, products and powers

Answer 7

Question 8

Given if z = x/y then g_z = g_x - g_y, then what would be the implication if g_x = g_y? or if g_x>g_y?

Answer 8

If g_x = 0.02 and g_y = 0.02, then the numerator and denominator are growing at the same rate, implying the ratio must be constant.

If g_x = 0.05 and g_y = 0.02, then the numerator is growing faster than the denominator, implying the ratio will grow by 3% per year (0.05-0.02).

Question 9

If z = x × y then g_z = g_x + g_y

What does this imply?

Answer 9

z will grow faster than x and y, for all cases.

Question 10

Pattern in growth rules

Answer 10

The mathematical operations on the growth rates are one level “simpler” than those for the variable themselves.

Question 11

Answer 11